PLEASE HELP......

Question

QUESTION 1: An future probe to HD 183579b (a new exoplanet) tosses a rock horizontally with a speed of 8.95m/s. The rock falls through a vertical distance of 2.35m and lands horizontal distance of 12.57m from the astronaut. What is the acceleration of gravity on Trappist-1bHD183579b ?

QUESTION 2:Cucmber Falls at Ohiopyle State Park east of Pittsburgh is approximately 10.m high. If the Cucumber Run is flowing horizontally at 1.20m/s just before going over the falls, what is the overall velocity of the water when it hits the bottom?

Answer 1

Both question refer to a situation of an object being propelled horizontally,

then falling under the action of gravity.

In both cases the trajectory is a parabola resulting from

- horizontal movement with constant velocity which would happen in the absence of gravity,

- vertical fall due to gravity, which would happen in the absence of any initial velocity.

Let

h be the starting height of the object,

v be the starting velocity,

d be the horizontal distance between hitting the ground,

g be gravitational acceleration,

x(t) be the horizontal distance after time t,

y(t) be the vertical height after time t,

t₁ be the time it takes to hit the ground.

By definition of velocity,

x(t) = vt

By definition of acceleration

y(t) = h - gt²/2

By definition of t₁

y(t₁) = 0

From that we can calculate t₁:

h - gt₁²/2 = 0

t₁ = √(2h/g)

By definition of d

x(t₁) = d

vt₁ = d

v√(2h/g) = d

We use the resulting equation for both questions

QUESTION 1:

v = 8.95 m/s

h = 2.35 m

d = 12.57

g = 2h(v/d)² = 2×2.35×(8.95/12.57)² = 2.38 m/s²

QUESTION 2:

v = 1.2 m/s

h = 10 m

g = 9.81 m/s²

d = v√(2h/g) = 1.2×√(2×10/9.81) = 1.7 m